A Semantic Investigation of Geometric Terminology in School Mathematics

학교 수학 기하 용어의 의미론적 탐색 - 기하 용어의 역사적 변천 및 국제 비교를 중심으로 -

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.